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Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

In soliton theories [

The equation is widely used in many physical branches, such as conformal field theory, two-dimensional quantum gravity, and conserved current of Liouville equation [

The outline of the paper is organized as follows. In Section

In this part, we consider a dependent variable transformation of 2DSK equation

Therefore, if

These sets lead to guarantee of the well-defined function

where the quadratic function

In this class of lump solutions,

Note that solutions in (

The plots are shown in Figure

Profiles of (

In Section

through substituting (

Under the transformation

By taking special choices of these parameters, the dynamic plots of collision between lump and one stripe soliton are depicted in Figure

Evolution plot of (

We study the collision between lump and one stripe soliton; on that basis, we begin to discuss the collision between lump and a pair of stripe solitons. In this section, we redefine

Through substituting solution (

Once again, by substituting (

In Figure

Evolution plot of (

Figure

Through Hirota bilinear form and symbolic calculation, we investigate the (2+1)-dimensional Sawada-Kotera equation. Its lump solutions are provided first, and the analyticity and localization of the resulting solutions are guaranteed by two determinant conditions. And then the interaction solutions between lump solutions and one stripe soliton are obtained and the results show that lump will be drowned or swallowed by the stripe soliton. Furthermore, we study the interaction solutions between lump solutions and a pair of solitons. In the beginning, there exist a pair of resonance stripe solitons; lump is hidden in one of the solitons. As time goes on, lump propagates gradually and it tangles with one of the resonance stripe solitons. When

In future work, we will be devoted to investigating the interaction solutions between lump solutions and other solutions to some equations. These problems will be worth discussing.

The authors declare that they have no conflicts of interest.

This work is supported by National Natural Science Foundation of China under Grant nos. 11271211 and 11435005 and K. C. Wong Magna Fund in Ningbo University.